Given:
Equation 1: x + 3y = 4
Equation 2: 2x + 6y = 7
Both the equations are in the form of:
a1x + b1y = c1 & a2x + b2y = c2 where
a1 & a2 are the coefficients of x
b1 & b2 are the coefficients of y
c1 & c2 are the constants
According to the problem:
a1 = 1
a2 = 2
b1 = 3
b2 = 6
c1 = 4
c2 = 7
Comparing the ratios of the coefficients we see:
On seeing equation (i), (ii) and (iii) we find
Conclusion:
The system of linear equations has no solutions.
The given system of linear equations will have no solution for all values of x and y